Air at 400kPa, 970 K enters a turbine operating at steady state and exits at 100 kPa, 670 K. Heat transfer from the turbine occurs at an average outer surface temperature of 315 K at the rate of 30 kJ per kg of air flowing. Kinetic and potential energy effects are negligible. For air as an ideal gas with Cp = 1.1 Kj/kg * K, determine

(a) the rate power is developed, in kJ per kg of air flowing, and
(b) the rate of entropy production within the turbine, in kJ/kg per kg of air flowing.

a

The rate of work developed is

b

The rate of entropy produced within the turbine is  

Explanation:

     From  the question we are told

          The rate at which heat is transferred is

the negative sign because the heat is transferred from the turbine

          The specific heat capacity of air is

          The inlet temperature is  

          The outlet temperature is

           The pressure at the inlet of the turbine is

          The pressure at the exist of the turbine is

           The temperature at outer surface is

         The individual gas constant of air  R with a constant value

The general equation for the turbine operating at steady state is \

h is the enthalpy of the turbine and it is mathematically represented as          

The above equation becomes

Where is the heat transfer from the turbine

            is the work output from the turbine

            is the mass flow rate of air

              is the rate of work developed

Substituting values

The general balance  equation for an entropy rate is represented mathematically as

          =>          

    generally

substituting for

                      Where is the rate of entropy produced within the turbine

 substituting values

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